課程名稱︰量子力學二 課程性質︰必修 課程教師︰高涌泉 開課學院：理學院 開課系所︰物理所 考試日期（年月日）︰2014/06/19 考試時限（分鐘）：130 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 1. a)What is the so-called bonding molecular orbital of the hydrogen molecule ion? What is the anti-bonding molecular orbital? 1 3 b)Is the first excited state of helium S_0 or S_1? Why? c)Is the total-spin state of the two electrons in the ground state for the hydrogen molecule a spin-0 or a spin-1 state? Why? 2.Use the Born approximation to determine the differential cross section for the potential energy C V = ─── r^2 where C is a constant, corresponding to a 1/r^3 force. 3.Calculate 〈n_{k,s}│E│n_{k,s}〉and〈n_{k,s}│E^2│n_{k,s}〉where E is the electric field operator and │n_{k,s}〉is the state with n_{k,s} photons, each with momentum hbar k and polarization s. 4.The Hamiltonian for a charge q in a 1-dimensional harmonic oscillator in a classical time-dependent electric field is given by H = H_0 + H_1 where (p_x)^2 1 2 2 H_0 = ──── + ── mω x 2m 2 and H_1 = -q x│E│exp(-t/τ). Suppose that at t = 0 the oscillator is in the n = 0 ground state. Treat H_1 as a perturbation. Use the time-dependent perturbation theory to calculate the probability to first order that the oscillator is in an excited state at t = ∞. 5.Explain a)The optical theorem. b)The electric dipole transition. --

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